Budaj earned his eighth career shutout and first this season in his fifth start. The shutout was Colorado's fourth. It was also Budaj's 84th career victory, which tied him with Stephane Fiset for the fourth-most wins in franchise history.
The Blues, who have an NHL-worst 5-9-3 home mark, were coming off two road victories that came by shootout. They have yet to win three games in a row this season. It also was the third time the Blues have been blanked on home ice this season.
Colorado grabbed the lead late in the first period when Stewart deflected in Kyle Quincey's point shot with 10.9 seconds left in the period to give the Avs a 1-0 lead. Colorado won a faceoff in the Blues zone to set up Quincey's one-timer, which Stewart deflected over Chris Mason's left shoulder.
Stastny gave Colorado a 2-0 lead 6:08 into the second by knocking a rebound into an empty net after Mason was knocked from the crease by Wolski, who got a shove from the Blues' David Backes.
Stewart scored his second of the game at 13:53 of the second, as he was able to redirect in Liles' shot from the right point for a 3-0 lead.
Duchene, the No. 3 overall pick in the 2009 draft, netted his ninth of the season at 12:44 of the third with a shot from the left circle that beat Mason through his pads.
NOTES: Stewart has 13 points in the last nine games. ... Wolski has a point in seven straight games and 11 of the last 12. ... Duchene has nine points in the last seven games, including six goals. ... Blues LW Keith Tkachuk has 52 points in 53 career games against Colorado. ... Blues D Eric Brewer (back) was placed on injured reserve and will miss two to four weeks. ... Blues C Patrik Berglund played in his 100th NHL game. ... Of Colorado's 32 games this season, 21 of them have been on the road, most in the NHL. ... Colorado RW Darcy Tucker skated in his 900th NHL game. ... Colorado G Craig Anderson (neck) missed his third consecutive game.